# [1]赵中华,王岩青.预处理子空间迭代法[J].东南大学学报(自然科学版),2003,33(4):511-513.[doi:10.3969/j.issn.1001-0505.2003.04.032] 　Zhao Zhonghua,Wang Yanqing.Preconditioning subspace iteration method[J].Journal of Southeast University (Natural Science Edition),2003,33(4):511-513.[doi:10.3969/j.issn.1001-0505.2003.04.032] 点击复制 预处理子空间迭代法() 分享到： var jiathis_config = { data_track_clickback: true };

33

2003年第4期

511-513

2003-07-20

## 文章信息/Info

Title:
Preconditioning subspace iteration method

1 南京财经大学应用数学系, 南京 210003; 2 解放军理工大学理学院, 南京 210016
Author(s):
1 Department of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210003, China
2 Institute of Science, PLA University of Science and Technology, Nanjing 210016, China

Keywords:

O241.6;O175.9
DOI:
10.3969/j.issn.1001-0505.2003.04.032

Abstract:
The problem of computing a few of the largest(or smallest)eigenvalues of a large sparse symmetric matrix is investigated. The preconditioning techniques for computing approximation of the large symmetric matrix are introduced, and improved algorithm and its convergence are presented. The convergence rate of subspace iteration method used to compute eigenvalues problem is confined when the distribution range of eigenvalues is large.In order to accelerate the convergence rate of the subspace iteration method, the preconditioning matrix is used to impact the residual matrix obtained from the iteration procedure, so the distribution of eigenvalues is improved. Having discussed the application of preconditioning techniques to the subspace iteration method, the preconditioning subspace iteration method is presented. Our numerical experiments show that the new method is more effective in convergence of algorithm. And it decreases the computation cost and computation time.

## 参考文献/References:

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Zhao Zhonghua.Subspace iteration accelerated by using chebyshev polynomids [J]. J NUAA,2002, 34(2):197-200.(in Chinese)
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